Two wires of copper have lengths L and 2L and cross sectional area 2A and A, respectively. The ratio of their specific resistance would be-
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1:1
Specific resistance (resistivity) \( \rho \) is a property of the material and its temperature. It does not depend on the length or the area of cross-section of the wire.
Both wires are of copper, so they have the same resistivity, and the ratio is 1:1.
Why the other options are incorrect
Option (1) 1:2 — Incorrect. 1:2 is the ratio of the lengths; length does not change the resistivity.
Option (2) 1:8 — Incorrect. 1:8 does not follow from the data; for the same material the ratio of resistivities is always 1:1.
Option (4) 1:4 — Incorrect. 1:4 is the ratio of the resistances, \( R = \rho L/A \): \( R_1 : R_2 = \frac{L}{2A} : \frac{2L}{A} = 1:4 \). The question asks for the specific resistance, not the resistance.
NCERT (2026-27):
Ohm’s Law – “… Combining Eqs. (3.5) and (3.7), we have
\( \displaystyle R \propto \frac{l}{A} \qquad (3.8) \)
and hence for a given conductor
\( \displaystyle R = \rho\,\frac{l}{A} \qquad (3.9) \)
where the constant of proportionality ρ depends on the material of the conductor but not on its dimensions. ρ is called resistivity.”